Patients arrive at a dentist clinic according to a Poisson process {X (t) :1 2 0} with parameter A: that is, on average A patients arrive per hour. The receptionist at the clinic notices that there are never two patients arriving at the same time. (a) Show that, mathematically, this observation is always correct. (b) Let to > t1 2 0, ti, t2 ( R., and n2 2 m 2 0, m, n2 E Z. Show that, if no patients arrive by time to, the probability that my patients arrive by time to is 12 P(X(t]) = n1 X(t2) = n2) = (c) Suppose that at a different clinic, patients arrive according to a Poisson process with a different parameter, , and we would like to determine the conditional probability in part (b) for that clinic. Would you have a different result? Give an intuitive explanation to your